We present an explicit pseudorandom generator for oblivious, read-once, width-$3$ branching programs, which can read their input bits in any order. The generator has seed length $\tilde{O}( \log^3 n ).$ The previously best known seed length for this model is $n^{1/2+o(1)}$ due to Impagliazzo, Meka, and Zuckerman (FOCS '12). Our ... more >>>

Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP is in NP/poly occurs, there is no AND-compression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NP-complete parameterized problems. We present a simple proof of this result.

An AND-compression is ... more >>>

We provide the first communication lower bounds that are sensitive to the network topology for computing natural and simple functions by point to point message passing protocols for the `Number in Hand' model. All previous lower bounds were either for the broadcast model or assumed full connectivity of the network. ... more >>>